Say you're in a one-table poker tournament with nine players, where the top three players get paid (with a payout structure something like this). There are four players remaining: one with a short stack, two with a ton of chips, and you, somewhere in the middle. Say you are dealt pocket aces (the best starting hand). Many players in this situation would fold to avoid the risk of busting out, because there's someone else so close to going broke and thus guaranteeing you some prize money.
For most poker players I know, cashing is the ultimate goal, leading to extreme risk aversion when they're on the bubble. But they would do better by being aggressive in such lopsided situations. In the long run, playing pocket aces has a high expected value. If you played this situation a thousand times, a few times you'll get unlucky and bust out, but you also finish in first a lot more than you otherwise would have.
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